The paper is partly motivated by recent pump-probe experiments with ultrashort laser pulses on antiferromagnetic FeRh that have shown the generation of magnetization within a subpicosecond time scale. On the other hand, the physical mechanism of the thermal antiferromagnetic-ferromagnetic (AFM-FM) phase transition in FeRh, known for many decades, remains a topic of controversial discussions. The selection of the magnetic degrees of freedom as well as the treatment of the magnetic excited states differ strongly in recent models by different authors. We report a density functional theory (DFT) investigation of FeRh. For the study of excited states, DFT calculations with constraints imposed on the directions and values of the atomic moments are employed. We show that the formation of the Rh moment as a consequence of the AFM-FM phase transition cannot be described with the Stoner picture. Instead, an implicit spin splitting of the Rh states takes place in the AFM phase, resulting in the intra-atomic spin polarization of the Rh atoms. This property is a consequence of the strong hybridization between Rh and Fe states. The Fe-Rh hybridization is an important factor in the physics of FeRh. We demonstrate that the ferromagnetic Fe-Rh exchange interaction is robust with respect to the crystal volume variation, whereas the antiferromagnetic Fe-Rh exchange interaction is strongly volume dependent. These different volume dependencies of the competing exchange interactions lead to their strong compensation at certain crystal volume. We perform Monte Carlo simulations and show that the calculated thermodynamics depends on the way the magnetic degrees of freedom are selected. We argue that the excited states resulting from the variation of the value of the Rh moment treated as degree of freedom are important for both the equilibrium thermodynamics of FeRh and the femtomagnetic phenomena in this system. We also study the spin mixing caused by spin-orbit coupling. The obtained value of the Elliott-Yafet spin-mixing parameter is comparable with earlier calculations for the ferromagnetic 3d metals. We draw the conclusion that the Elliott-Yafet mechanism of the angular-momentum transfer between electrons and lattice plays an important role in the femtomagnetic properties of FeRh.